Effect of quantum nuclear motion on hydrogen bonding

Abstract

This work considers how the properties of hydrogen bonded complexes, X-H· · · Y, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (X) and acceptor (Y) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H· · · O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4 − 3.0Å, i.e., from strong to weak hydrogen bonds. The position of the proton (which determines the X-H bond length) and its longitudinal vibrational frequency, along with the isotope effects in both are described quantitatively. An analysis of the secondary geometric isotope effect, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of bending modes is also considered: their quantum effects compete with those of the stretching mode for weak to moderate Hbond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several trends.

Effect of hydrogen bonding on the infrared absorption intensity of OH stretch vibrations

“…Within our diabatic model, as the H-bond strengthens from R = 3.0Å to about R = 2.45Å, deuteration leads to a progressive increase in the O-O equilibrium distance of up to about 0.04Å. Though small in magnitude, it was found to yield significant H/D frequency effects 30 . This is because changing R changes the shape of the OH stretch potential, and small changes in R are particularly significant in the regime of low-barrier H-bonds where the energy barrier is comparable to the OH stretch zero point energy.…”

“…The above discussion is based on Figure 3 in Ref. 30 which shows the different potentials and low-lying vibrational energies for R = 2.3, 2.45, 2.5, 2.9Å.…”

“…It was shown in subsequent work 30,31 that it affords a quantitative description of the correlations observed 32 between the OO distance (R) and OH bond lengths (r), the frequencies of OH vibrations (both stretch and bend), and H/D isotope effects for a diverse range of chemical compounds 30,31 . We use the same notation and parameters as in Ref.…”

“…However, we use these labels at all R; see Ref. 30 for further details. For the asymmetric cases, we simply drop the ± subscript.…”

“…. 30 . The corresponding transition dipole moment for a transition n f ← n i , is only nonzero when n f −n i is odd, for which A if ∝ (n 2 f n 2 i )/(n 2 f −n 2 i ) 3 is box-length independent.…”